1

IIT-JEE 1994

Subjective

+5

-0

Consider the following statements connecting a triangle $$ABC$$

(i) The sides $$a, b, c$$ and area $$\Delta $$ are rational.

(ii) $$a,\tan {B \over 2},\tan {c \over 2}$$ are rational.

(iii) $$a,\sin A,\sin B,\sin C$$ are rational.

Prove that $$\left( i \right) \Rightarrow \left( {ii} \right) \Rightarrow \left( {iii} \right) \Rightarrow \left( i \right)$$

2

IIT-JEE 1994

Subjective

+4

-0

A tower $$AB$$ leans towards west making an angle $$\alpha $$ with the vertical. The angular elevation of $$B$$, the topmost point of the tower is $$\beta $$ as observed from a point $$C$$ due west of $$A$$ at a distance $$d$$ from $$A$$. If the angular elevation of $$B$$ from a point $$D$$ due east of $$C$$ at a distance $$2d$$ from $$C$$ is $$\gamma $$, then prove that $$2$$ tan $$\alpha = - \cot \beta + \cot \gamma $$.

3

IIT-JEE 1993

Subjective

+5

-0

An observer at $$O$$ notices that the angle of elevation of the top of a tower is $${30^ \circ }$$. The line joining $$O$$ to the base of the tower makes an angle of $${\tan ^{ - 1}}\left( {1/\sqrt 2 } \right)$$ with the North and is inclined Eastwards. The observer travels a distance of $$300$$ meters towards the North to a point A and finds the tower to his East. The angle of elevation of the top of the tower at $$A$$ is $$\phi $$, Find $$\phi $$ and the height of the tower.

4

IIT-JEE 1992

Subjective

+4

-0

Three circles touch the one another externally. The tangent at their point of contact meet at a point whose distance from a point of contact is $$4$$. Find the ratio of the product of the radii to the sum of the radii of the circles.

Questions Asked from Properties of Triangle (Subjective)

Number in Brackets after Paper Indicates No. of Questions

IIT-JEE 2003 (1)
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IIT-JEE 1978 (1)

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